Question

Harry rode his broom from Hogwarts Castle to Ron’s home. He was going to arrive at 3:00 pm, but

he spent 2/3 of the planned time covering 3/4 of the distance. After that, he rode more slowly and
arrived exactly as expected. What is the ratio of the speed for the first part of the journey to the
speed for the second part?

Answer 1

To solve this problem, we can use the formula:

Speed = Distance / Time

Let's say the total distance from Hogwarts Castle to Ron's home is D, and let's assume Harry's speed for the first part of the journey is S1 and his speed for the second part of the journey is S2.

So, for the first part of the journey, Harry covered 3/4 * D distance in 2/3 of the time, and for the second part, he covered 1/4 * D distance in 1/3 of the time.

First part:

Speed1 = (3/4 * D) / (2/3)

Speed1 = (3/4 * 3/2 * D) / 1

Speed1 = (9/8) * D

Second part:

Speed2 = (1/4 * D) / (1/3)

Speed2 = (1/4 * 3) * D

Speed2 = (3/4) * D

So, the ratio of the speed for the first part of the journey to the speed for the second part is:

Speed1 : Speed2

(9/8) * D : (3/4) * D

9/8 : 3/4

9/8 : 3/4

\[(9/8) / (3/4) = 9/8 * 4/3 = 3/2\]

The ratio of the speed for the first part of the journey to the speed for the second part is 3:2.